Darcy Inc. has just paid out a dividend (annual) of$2.40 per share. The company
ID: 2770815 • Letter: D
Question
Darcy Inc. has just paid out a dividend (annual) of$2.40 per share. The company is in a state of rapid growth of12%, which can only be sustained for the next 4 years. Afterthat, its earnings growth is expected to drop to a long-termsustainable growth of 4%. Its dividends will grow at the samerate as earnings, as the firm is expected to maintain its payoutratio. As an analyst, estimate the fair price for Darcy stocktoday. Use the following additional information: the 10-yearTreasury rate is 3.5%; the beta for the company’s stock(based on the regression of its returns on those of the S&P 500Index) is 1.45, and the estimate of returns on the S&P 500Index is 14%. This is from a final I took last year, trying to back into theanswer Darcy Inc. has just paid out a dividend (annual) of$2.40 per share. The company is in a state of rapid growth of12%, which can only be sustained for the next 4 years. Afterthat, its earnings growth is expected to drop to a long-termsustainable growth of 4%. Its dividends will grow at the samerate as earnings, as the firm is expected to maintain its payoutratio. As an analyst, estimate the fair price for Darcy stocktoday. Use the following additional information: the 10-yearTreasury rate is 3.5%; the beta for the company’s stock(based on the regression of its returns on those of the S&P 500Index) is 1.45, and the estimate of returns on the S&P 500Index is 14%. This is from a final I took last year, trying to back into theanswerExplanation / Answer
Dividend just paid (D0) = $2.40 per share
The Company is in a state of rapid growth of 12% which can onlybe sustained for the next 4 years
Expected dividend growth rate = 4% per year
Calculating Expected dividend in each of the Next 4Years:
Dividend in First year (D1) = $2.40 (1+0.12) = $2.688
Dividend in Second year(D2) = $2.688 (1+0.12) = $3.01056
Dividend in Third year (D3) = $3.01056(1+0.12) = $3.3718
Dividend in fourth year (D4) = $3.3718(1+0.12) = $3.7764
After 4 years the earnings growth is expected to drop to along-term sustainable growth of 4%
Dividend in fifth year (D5) = $3.7764 (1+0.04) = $3.9275
Dividend in sixth year (D6) = $3.9275 (1+0.04) = $4.0846
Calculating Required Return (RE) using SMLapproach:
Risk-free rate(Rf) = 3.5%
Stockbeta = 1.45
Expected return on Market(RM) = 14%
Required return (RE) = Rf + ß (RM – Rf)
Required return (RE) = 0.035 +1.45 (0.14 – 0.035)
= 0.035 +1.45(0.105)
= 0.035 +0.15225
= 0.1872 (or) 18.72%
Required return(RE) = 18.72%
Stock Price (P5) = D6 / (0.1872– 0.04)
= $4.0846 / 0.1472 = $27.75
Stock Price(P5) = $27.75
Calculating Today’s StockValue:
P0 = [D1/(1+R) +D2/(1+R)2 +D3/(1+R)3 +D4/(1+R)4 +D5/(1+R)5 +P5/(1+R)5]
= [$2.688/(1.1872) +$3.01056/(1.1872)2 + $3.3718/(1.1872)3 +$3.7764/(1.1872)4
= + $3.9275 / (1.1872)5 + $27.75 / (1.1872)5
= $2.26 + $2.13599 + $2.015+ $1.90 +$1.66 + $11.766
= $21.74
Today’s Stock Value(P0) = $21.74
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